Only 9% of women with positive mammograms have breast cancer. Even doctors get this wrong. If you ask them, two-thirds will erroneously conclude that a p < 0.05 result implies a 95% chance that the result is true.2 But as you can see in these examples, the likelihood that a positive mammogram means cancer depends on the proportion of women who actually have cancer. And we are very fortunate that only a small proportion of women have breast cancer at any given time.
